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Setler [38]
2 years ago
14

1

Mathematics
1 answer:
Whitepunk [10]2 years ago
5 0

Answer:

C. M(x) = 4x + 4

Step-by-step explanation:

Find the rate of change/slope (m) using two pairs (1, 8) and (2, 12):

slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 8}{2 - 1} = \frac{4}{1} = 4

(Note: M(x) = y)

Find y-intercept (b) by substituting x = 1, M(x) = 8, and m = 4 in M(x) = mx + b.

Thus:

8 = (4)(1) + b

8 = 4 + b

Subtract 4 from each side

8 - 4 = b

4 = b

b = 4

substitute m = 4, and b = 4 in M(x) = mx + b, to get the equation that models the relationship.

The equation would be:

✅ M(x) = 4x + 4

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1 doller bill and a 10 doller bill and for quarters makes what?
spin [16.1K]
12 dollars.

1+10=11
Then 4 quarters is $1 so you then add a dollar to get
$12
7 0
1 year ago
A manufacturer is planning to sell a new product at the price of 210 dollars per unit and estimates that if x thousand dollars i
sattari [20]

Answer:

Development costs: $2757

Promotion costs: $3155

Step-by-step explanation:

This might seem like a two-variable problem, but in actuality it's not - because the demand function is a sum of two components, each being independent and using only one variable, we can solve for the two separately.

Moreover, the price per unit and cost per unit is constant, so each product yields exactly $80 ($210 - $130).

Let's solve separately.

We need to maximize:

$80 * 160y/(y+4) - 1000y = $12800 * y/(y+4) - $1000*y

$80 * 170x/(x+7) - 1000x = $13600 * x/(x+7) - $1000*x

Let's go:

$12800 * y/(y+4) - $1000*y = $12800 * (1 - 4/(y+4)) - $1000y = $12800 - $51200/(y+4) - $1000*y

we analyze the derivative. $12800 is a constant, so we can skip it. Derivative of 1/(y+4) is -(y+4)^-2, derivative of $1000y is $1000.

deriv = $51200/(y+4)/(y+4) - $1000

We find the changepoints by analyzing $51200/(y+4)/(y+4) - $1000 = $0. We don't need to worry about y+4 = 0 because we cannot spend negative money on development/advertisement.

(y+4)^2 = $51.2

y+4 ~= 7.155417528 (or -y-4 = 7.1554... but it doesn't make sense because negative budget so we don't analyze).

y ~= 3.155417528

lastly, we should check that it's actually a maximum there - but it is, the original function goes to negative infinity.

rounding $1000y to the nearest dollar gives us $3155

Let's do the same for x:

$13600 * x/(x+7) - $1000*x = $13600 * (1 - 7/(x+7)) - $1000x = $13600 - $95200/(x+7) - $1000*x

deriv = $95200/(x+7)/(x+7) - $1000

$95200/(x+7)/(x+7) - $1000 = $0

(x+7)^2 = 95.2

(x+7) ~= 9.75704873412

x ~= 2.75704...

rounding $1000x to the nearest dollar yields $2757

3 0
2 years ago
A system of equations is given below:
My name is Ann [436]
Solving by substitution:

y = 4x - 3 

2x + 7y = 41

Let us substitute the first equation y = 4x - 3  into the second.

2x + 7y = 41

2x + 7(y = 4x -3) = 41

2x + 7(4x -3) = 41

So that's the third option.

I hope this helps.
4 0
3 years ago
Read 2 more answers
Evaluate: (8y+5) -2z; if y =3 and z =9
iVinArrow [24]

Answer:

11

Step-by-step explanation:

(8y + 5) - 2z

y = 3, z = 9

Let's plug in the given values.

(8(3) + 5) - 2(9)

First let's multiply.

(24 + 5) - 18

Now simplify within the parentheses.

29 - 18

Subtract.

11

This is your answer.

Hope this helps!

5 0
3 years ago
The pet store has 18 dogs toys for sale. 10 toys are frisbees and the rest are bones. What is the ratio of bones to frisbees in
tangare [24]

Answer:

4 : 5

Step-by-step explanation:

18 - 10 = 8 (Bones)

Bones to frisbees

8 : 10

Simplest form which is divided by 2 for each number:

4 : 5

5 0
3 years ago
Read 2 more answers
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